A method of commutating a motor includes calculating an adjustment electrical angle, and utilizing the adjustment electrical angle in a common set of commutation equations so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor.
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1. A method of commutating a motor comprising:
calculating an electrical angle offset;
applying the electrical angle offset to an electrical angle in a common set of commutation equations for a three phase motor for producing a one dimensional force so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor; and
varying the electrical angle offset as applied within the common set of commutation equations to control the three phase motor so that both of the two dimensional forces produced by the motor are independently controllable.
17. An apparatus for commutating a motor comprising:
circuitry for calculating an electrical angle offset; and
an amplifier operable to apply the electrical angle offset to an electrical angle in a common set of commutation equations for a three phase motor for producing a one dimensional force so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor,
the amplifier configured to vary the electrical angle offset as applied within the common set of commutation equations to control the three phase motor so that both of the two dimensional forces produced by the motor are independently controllable.
29. A motor comprising:
windings commutated by a controller, the controller having:
circuitry for calculating an electrical angle offset; and
an amplifier operable to apply the electrical angle offset to an electrical angle in a common set of commutation equations for a three phase motor for producing a one dimensional force so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor,
the amplifier further operable to vary the electrical angle offset as applied within the common set of commutation equations to control the three phase motor so that both of the two dimensional forces produced by the motor are independently controllable.
41. A substrate processing apparatus comprising:
a controller for commutating a motor including:
circuitry for calculating an electrical angle offset; and
an amplifier operable to apply the electrical angle offset to an electrical angle in a common set of commutation equations for a three phase motor for producing a one dimensional force so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor,
the amplifier further operable to vary the electrical angle offset as applied within the common set of commutation equations to control the three phase motor so that both of the two dimensional forces produced by the motor are independently controllable.
13. A method of commutating a motor comprising:
calculating an electrical angle offset;
entering the electrical angle offset as an adjustment to an electrical angle into commutation equations for a three phase motor for commutating motor windings of the three phase motor to produce forces in the motor in one dimension, wherein the electrical angle offset is determined so that the commutation equations for producing forces in the three phase motor in the one dimension are common with commutation equations for simultaneously producing forces in the motor in two dimensions; and
varying the electrical angle offset as applied within the common commutation equations to control the three phase motor so that both of the two dimensional forces produced by the motor are independently controllable.
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The embodiments described herein relate to a method and system for commutation of an electromagnetic propulsion and guidance drive, in particular for a magnetically levitated material transport platform.
A schematic plan view of a conventional substrate processing apparatus is shown in
The disclosed embodiments are directed to a method of commutating a motor including calculating an adjustment electrical angle, and utilizing the adjustment electrical angle in a common set of commutation equations so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor.
In another embodiment, a method of commutating a motor includes calculating an adjustment electrical angle, and entering the adjustment electrical angle into commutation equations for commutating motor windings to produce forces in the motor in at least one dimension, wherein the adjustment electrical angle is determined so that commutation equations for producing forces in the motor in but one of the at least one dimension are common with commutation equations for simultaneously producing forces in the motor in two of the at least one dimension.
In another embodiment, an apparatus for commutating a motor includes circuitry for calculating an adjustment electrical angle, and an amplifier operable to utilize the adjustment electrical angle in a common set of commutation equations so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor.
In still another embodiment, a motor has windings commutated by a controller, where the controller includes circuitry for calculating an adjustment electrical angle, and an amplifier operable to utilize the adjustment electrical angle in a common set of commutation equations so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor.
In yet a further embodiment, a substrate processing apparatus has a controller for commutating a motor including circuitry for calculating an adjustment electrical angle, and an amplifier operable to utilize the adjustment electrical angle in a common set of commutation equations so that the common set of commutation equations is capable of producing both one and two dimensional forces in the motor.
The foregoing aspects and other features of the present invention are explained in the following description, taken in connection with the accompanying drawings, wherein:
FIGS. 13B1-13B2 are schematic views of respective magnet array(s) in accordance with different exemplary embodiments;
FIG. 13D1-13D2 are schematic views of respective winding arrangements in accordance with different exemplary embodiments;
The disclosed embodiments relate to a propulsion and guidance system for a magnetically levitated material transport platform. Motor force equations and motor commutation equations, including expressions for calculation of motor control parameters based on specified propulsion and guidance forces, are provided for both two dimensional and three dimensional motor configurations.
The disclosed embodiments include adjusting an electrical angle used to drive a common set of commutation functions with an electrical angle offset so that the same motor commutation functions may be used for producing at least a one dimensional propulsion force in the x-direction, two dimensional forces including a propulsion force in the x-direction and a guidance force in the y-direction, and three dimensional forces including propulsion forces in both the x-direction and a z-direction and a guidance force in the y-direction.
In other words, by adjusting the electrical angle with the electrical angle offset, at least one, two, and three dimensional forces may be produced in the motor using a common set of commutation equations.
In particular, motor force equations, motor commutation equations, and motor control parameter calculations are provided for two dimensional motor configurations to produce propulsion in the x-direction by Lorentz forces, with guidance in the y-direction by Lorentz and Maxwell forces. Another embodiment includes motor force equations, motor commutation equations, and motor control parameter calculations to produce propulsion in the x-direction by Lorentz forces, with guidance in the y-direction by Maxwell forces for two dimensional motor configurations. Still another embodiment includes motor force equations, motor commutation equations, and motor control parameter calculations to produce propulsion in the x-direction with guidance in the y-direction primarily utilizing Lorentz forces for two dimensional motor configurations.
Similarly, for three dimensional motor configurations, motor force equations, motor commutation equations, and motor control parameter calculations are provided to produce propulsion in the x-direction, lift in the z-direction by Lorentz forces, with guidance in the y-direction by Lorentz and Maxwell forces. Additional embodiments include motor force equations, motor commutation equations, and motor control parameter calculations for three dimensional motor configurations to provide propulsion in the x-direction and lift in the z-direction by Lorentz forces, with guidance in y-direction by Maxwell forces. Yet another embodiment includes motor force equations, motor commutation equations, and motor control parameter calculations for three dimensional motor configurations that provide propulsion in the x-direction, lift in the z-direction, and guidance in the y-direction all utilizing Lorentz forces.
Further embodiments include motor force equations, motor commutation equations, and motor control parameter calculations for phase commutation with open loop stabilization, including open loop roll stabilization, open loop pitch stabilization with discrete forces, and open loop pitch stabilization with distributed forces.
Turning again to
The EFEM 14 may include a substrate transport apparatus (not shown) capable of transporting substrates from load ports 12 to load locks 16. The load ports 12 are capable of supporting a number of substrate storage canisters, for example conventional FOUP canisters or any other suitable substrate storage device. The EFEM 14 interfaces the transport chamber 18 through load locks 16. The EFEM 14 may further include substrate alignment capability, batch handling capability, substrate and carrier identification capability or otherwise. In alternate embodiments, the load locks 16 may interface directly with the load ports 12 as in the case where the load locks have batch handling capability or in the case where the load locks have the ability to transfer wafers directly from a FOUP to the lock. In alternate embodiments, other load port and load lock configurations may be provided.
Still referring to
At least one substrate transport apparatus 22 is integrated with the transport chamber 18. In this embodiment, processing modules 20 are mounted on both sides of the transport chamber 18, however, in other embodiments processing modules 20 may be mounted on one side of the chamber, may be mounted opposite each other in rows or vertical planes, may be staggered from each other on the opposite sides of the transport chamber 18, or stacked in a vertical direction relative to each other.
The transport apparatus 22 generally includes a single carriage 24 positioned in the transport chamber 18 for transporting substrates between load locks 16 and processing modules 20 or among the processing chambers 20. In alternate embodiments, multiple carriages may be utilized in a transport apparatus. Moreover, the transport chamber 18 may be capable of being provided with any desired length and may couple to any desired number of processing modules 20. The transport chamber 18 may also be capable of supporting any desired number of transport apparatus 22 therein and allowing the transport apparatus 22 to reach any desired processing module 20 on the transport chamber 18 without interfering with each other.
The transport chamber 18 in this embodiment has a generally hexahedron shape though in alternate embodiments the chamber may have any other suitable shape. The transport chamber 18 has longitudinal side walls 18S with ports formed therethrough to allow substrates to pass into and out of the processing modules 20. The transport chamber 18 may contain different environmental conditions such as atmospheric, vacuum, ultra high vacuum, inert gas, or any other, throughout its length corresponding to the environments of the various processing modules connected to the transport chamber. While a single transport chamber 18 is shown, it should be understood that any number of transport chambers may be coupled together in any configuration to accommodate substrate processing. It should also be understood that the transport chamber may extend inside one or more of the processing modules 20, load locks 16, or even load ports 12, or one or more of the processing modules 20, load locks 16, or load ports 12 may have its own transport chamber coupled to transport chamber 18, allowing the transport mechanism to enter or otherwise deliver substrates to the processing modules.
The transport apparatus 22 may be integrated with the transport chamber 18 to translate the carriage 24 along an x-axis extending between the front of the chamber 18F and the back of the chamber 18B. The transport apparatus may also provide guidance along a y-axis perpendicular to the x-axis. In other embodiment, the transport apparatus 22 may translate the carriage along the x-axis and along a z-axis extending out from the surface of the page, orthogonal to the x and y axes, and provide guidance along the y-axis.
The carriage 24 may transport substrates by themselves, or may include other suitable mechanisms for substrate transport. For example, carriage 24 may include one or more end effectors for holding one or more substrates, an articulated arm, or a movable transfer mechanism for extending and retracting the end effectors for picking or releasing substrates in the processing modules or load locks. In some embodiments the carriage 24 may be supported by linear support or drive rails which may be mounted to the side walls 18S, which may include the floor or top of the transport chamber and may extend the length of the chamber, allowing the carriage 24 to traverse the length of the chamber.
The transport chamber 18 may have a number of transport zones 18′, 18″ which allow a number of transport apparatus to pass over each other, for example, a side rail, bypass rail or magnetically suspended zone. The transport zones may be located in areas defined by horizontal planes relative to the processing modules. Alternately, the transport zones may be located in areas defined by vertical planes relative to the processing modules.
Turning to
Controller 200 drives the windings as described below resulting in the application of various forces. Thus, controller 200 drives the windings to actively produce desirable combinations of propulsion, lift and guidance forces for open and closed-loop control.
The disclosed embodiments may employ one or more linear drive systems which may simultaneously drive and suspend the transport apparatus such that the transport apparatus may be horizontally and vertically independently movable. Thus, multiple transport apparatus may be capable of passing each other and capable of transporting substrates independent of each other. In some embodiments each transport apparatus may be driven by a dedicated linear drive motor. The disclosed embodiments may, in addition or alternately, employ one or more rotary drive systems which may simultaneously drive and suspend the transport apparatus such that the transport apparatus may be horizontally and vertically independently movable.
The platen 324 may include for example one or more magnets 334 for interfacing the platen 324 with winding set 322. As may be realized, in alternate embodiments, the permanent magnets may be located on the stator and the windings may be located on the driven platen. A sensor 336, for example, a magneto-resistive or hall effect sensor, may be provided for sensing the presence of the magnets in platen 324 and determining proper commutation. Additionally, sensors 336 may be employed for fine position determination of platen 324.
A position feedback device 340 may be provided for accurate position feedback. Device 340 may be inductive or optical for example. In the instance where it is inductive, an excitation source 342 may be provided which excites a winding or pattern 346 and inductively couples back to receiver 344 via coupling between the pattern 346. The relative phase and amplitude relationship may be used to determine the location of platen 324. An identification tag 347, such as an IR tag may be provided that may be read by reader 348, provided at an appropriate station to determine platen identification by station.
In other embodiments the winding set 322 may be mounted to the platen 324 while the one or more magnets 334 may be mounted on the outside of or within the side wall 330 (which may include a top, side, or floor of the transport chamber 18). The one or more magnets 334 may be isolated from the chamber and from the platen 324 by the side wall 330. In other embodiments, the one or more magnets 334 may be located inside the transport chamber 18.
Magnets may be distributed on the platen 425 in any suitable configuration. As may be realized, in alternate embodiments the windings may be on the rotor and permanent magnets on the stator. The disclosed embodiments include at least two magnets 430 for interfacing the platen 425 with winding set 422. One or more sensors 435, for example, a magneto-resistive or hall effect sensor, may be provided for sensing the presence of the magnets 430 in platen 425 and determining proper commutation. Additionally, sensors 435 may be employed for fine position determination of platen 425.
In other embodiments the winding set 422 may be mounted to the platen 425 while the magnets 430 may be mounted to the stator 415. The one or more stator mounted magnets 430 may be isolated from the chamber and from the platen 425 by the side wall 330. In other embodiments, the magnets 430 may be located inside the transport chamber 18.
The platen 324, 425 of the embodiments of
For this exemplary embodiment, the motor force equations, motor commutation equations, and expressions for calculation of motor control parameters based on specified propulsion and guidance forces are for example as follows:
Motor Force Equations:
where:
Fx=Total force produced in x-direction (N)
Fy=Total force produced in y-direction (N)
Fxj=Force produced by phase j in x-direction, j=0, 1, 2 (N)
Fyj=Force produced by phase j in y-direction, j=0, 1, 2 (N)
ij=Current through phase j, j=0, 1, 2 (N)
Kfx=Phase force constant in x-direction (N/A)
KfyL=Lorentz phase force constant in y-direction (N/A)
KfyM=Maxwell phase force constant in y-direction (N/A2)
x=Position in x-direction (m)
y=Position in y-direction (m)
θ=Electrical angle (rad)
The motor commutation equation may be expressed for example as:
ij=I sin [θ(x)−Δ+(2π/3)j], j=0,1,2 (1.3)
where I and Δ control the magnitude and orientation of the motor force vector and:
I=Amplitude of phase current (A)
Δ=Electrical angle offset (rad)
As may be realized from examination of (1.3), in the example the disclosed embodiments include adjusting the electrical angle θ using the electrical angle offset Δ so that a guidance force along the y-axis may be generated concurrently with, but controllable independently from, the propulsion force along the x-axis. Thus, by adjusting the electrical angle θ with the electrical angle offset Δ, the same motor commutation equation for producing a pure propulsion force may be used to produce both a propulsion force and a guidance force that are substantially independently controllable from each other.
Sinusoidal phase currents in accordance with Equation (1.3) can be generated using space vector modulation (SVM), such as for the wye winding configuration, to optimize utilization of bus voltage
The resulting motor forces in the x and Y directions may be expressed for example as:
Fx=1.5IKfx(y)cos(Δ) (1.4)
Fy=1.5I[KfyL(y)sin(Δ)+IKfyM(y)] (1.5)
The substantially independent motor control parameters I and Δ in (1.4) and (1.5) may be derived for example as:
For purposes of the disclosed embodiments, all arc tangent functions (a tan) described herein may also be interpreted as a four quadrant inverse tangent functions (a tan 2). [Please fix the language as needed.]
Inequality (1.18) imposes a constraint for the desired forces Fx and Fy. This means, in order to have a solution I and Δ, such constraint is satisfied. Considering (1.13), (1.14) and (1.15), inequality (1.18) may be rewritten as:
The constraint (1.19) means that, in the exemplary embodiment, given a desired force along x-direction, there may be a minimum physical limit for the force along y-direction.
The platen 324 and forcer 321 in the embodiments of
As may be realized, the Maxwell force between the winding set 322, 422 and the ferromagnetic platen 324, 425 is attractive, hence an additional mechanism may be employed to produce a force in the opposite direction. This can be achieved, for example, by utilizing another winding set of the same type in a mirror configuration (not shown). In the exemplary embodiment there may be some coupling between the propulsion and guidance forces due to the constraint (1.19). For example, the current employed to produce some specified propulsion force may generate some guidance force. The additional winding set of similar type, disposed in a mirror configuration may also be used to balance the additional guidance force if desired, and thus resulting in substantially decoupled forces in the X-direction and Y-direction respectively for substantially any desired magnitude.
In this embodiment a force vector is produced in the x-y plane, including a propulsion component in the x-direction and a guidance component in the y-direction. In the linear propulsion embodiment 320 this enables control of the relative position of the ferromagnetic platen 324 with respect to the forcer 321 in the x-direction as well as the gap between the platen 324 and the forcer 321 in the y-direction. In the rotary propulsion embodiment 410, the applied forces provide control of the relative rotational position of the platen 425 in the x-direction, defined in this embodiment as a rotational direction in the plane of the x and y axes, and control of the gap between the platen 425 and the stator 415.
As mentioned above, in the linear propulsion embodiment 320 platen 324 may be supported in the z-direction by a suitable mechanism or structure. In the rotary propulsion embodiment 410, the platen or rotor 425 may be supported in the z-direction (perpendicular to the plane of the page) by a suitable mechanism or structure.
The embodiments of
The motor force equations for the embodiments of
where
Fx=Total force produced in x-direction (N)
Fy=Total force produced in y-direction (N)
Fxj=Force produced by phase j in x-direction, j=0, 1, 2 (N)
Fyj=Force produced by phase j in y-direction, j=0, 1, 2 (N)
ij=Current through phase j, j=0, 1, 2 (N)
Kfx=Phase force constant in x-direction (N/A)
Kfy=Phase force constant in y-direction (N/A2)
x=Position in x-direction (m)
y=Position in y-direction (m)
θ=Electrical angle (rad)
The motor commutation equation may be for example:
ij=I sin [θ(x)−Δ+(2π/3)j], j=0,1,2 (2.3)
where I and Δ are control parameters and:
I=Amplitude of phase current (A)
Δ=Electrical angle offset (rad)
It should be noted that equation (2.3) is the same as (1.3) and that adjusting the electrical angle θ using the electrical angle offset Δ produces a guidance force along the y-axis and a propulsion force along the x-axis. Thus, by adjusting the electrical angle θ with the electrical angle offset Δ, the same motor commutation equation for producing a pure propulsion force may be used to produce both a propulsion force and a guidance force that may be substantially decoupled from each other as previously described.
With the winding set 322 in a wye-configuration, sinusoidal phase currents in accordance with Equation (2.3) may be generated using space vector modulation. The resulting motor forces are:
Fx=1.5IKfx(y)cos(Δ) (2.4)
Fy=1.5I2Kfy(y) (2.5)
and motor force coupling of the propulsion and guidance forces may be represented as:
The independent control parameters I and Δ for particular forces in the x and y directions may be derived as:
I=√{square root over (Fy/[1.5Kfy(y)])} (2.8)
Δ=a cos {Fx/[1.5IKfx(y)]} (2.9)
In the linear propulsion embodiment 320 the relative position of the platen 324 with respect to the forcer 321 in the x-direction as well as the gap between the platen 324 and the forcer 321 in the y-direction are controlled in an independent manner. As mentioned above, the platen 324 and forcer 321 may be controlled to remain substantially parallel to each other, for example, utilizing any suitable mechanism. Similarly, in the rotary propulsion embodiment 410, the applied forces provide control of the relative rotational position of the platen 425 in the x-direction, defined in this embodiment as a rotational (e.g. tangential) direction in the plane of the x and y axes, and control of the gap between the platen 425 and the forcer 422. As may be realized, the gap with respect to the whole stator is a two-dimensional quantity (vector), whereas the gap with respect to an individual forcer segment is a scalar that can be controlled by the given forcer segment (although the other forcers are also contributing. The platen or rotor 425 may be supported in the z-direction (perpendicular to the plane of the page) by a suitable mechanism or structure.
The embodiments utilize Lorentz forces produced by applying position-dependent currents to the windings subject to the magnetic field of the permanent magnets.
The following motor force equations may be utilized:
where
Fx=Total force produced in x-direction (N)
Fy=Total force produced in y-direction (N)
Fxj=Force produced by phase j in x-direction, j=0, 1, 2 (N)
Fyj=Force produced by phase j in y-direction, j=0, 1, 2 (N)
ij=Current through phase j, j=0, 1, 2 (N)
Kfx=Phase force constant in x-direction (N/A)
Kfy=Phase force constant in y-direction (N/A)
x=Position in x-direction (m)
y=Position in y-direction (m)
θ=Electrical angle (rad)
In the exemplary embodiment, motor commutation equation may before example:
ij=I sin [θ(x)−Δ+(2π/3)j], j=0,1,2 (3.3)
where I and Δ control the magnitude and orientation of the motor force vector, respectively. More specifically:
I=Amplitude of phase current (A); and
Δ=Electrical angle offset (rad)
It should be noted that equations (3.3), (2.3), and (1.3) are the same. Thus, similar to the embodiments above, adjusting the electrical angle θ using the electrical angle offset Δ produces a guidance force along the y-axis and a propulsion force along the x-axis. Thus, by adjusting the electrical angle θ with the electrical angle offset Δ, the same motor commutation equation for producing a pure propulsion force may be used to produce both a propulsion force and a guidance force that are substantially decoupled from each other.
With the winding set 322, 422 in a wye configuration, sinusoidal phase currents in accordance with Equation (3.3) can be generated using space vector modulation.
The following motor forces are the result:
Fx=1.5IKfx(y)cos(Δ) (3.4)
Fy=1.5IKfy(y)sin(Δ) (3.5)
and the values of the independent control parameters I and Δ may be derived from:
I=√{square root over ([Fx/Kfx(y)]2+[Fy/Kfy(y)]2)}{square root over ([Fx/Kfx(y)]2+[Fy/Kfy(y)]2)}/1.5 (3.6)
Δ=a tan [FyKfx(y),FxKfy(y)] (3.7)
Referring now to
i=I sin [θ(x)−Δ+(π/3)i], i=0,1,2)
may be utilized in a manner similar to that described previously (see for example (1.1)-(1.23)) in order to generate similar force vectors as in the exemplary embodiments shown in
The embodiment in
The transport apparatus 1305 includes magnet platens 1335, 1340. Magnet platens 1335, 1340 may be arranged as an array of magnets and may extend along a length of opposing sides 1345, 1350, respectively, of transport apparatus 1305. In one embodiment, the array of magnets may be arranged with alternating north poles 1355 and south poles 1360 facing the winding sets. A position feedback system, for example, a suitable number of position sensors (e.g. Hall effect sensors 1390, 1395 may be provided for sensing the location, for example, the x, y, and z coordinates of the transport apparatus 1305. Other suitable sensor systems may be utilized.
FIGS. 13B1-13B2 show respectively different exemplary arrangements 1370, 1370′ of the array of magnets that may be used with the disclosed embodiments. In the exemplary embodiment shown in FIG. 13B1, the rows of magnets may be staggered or offset with alternating rows having the N and S polarities facing outward. In the exemplary embodiment shown in FIG. 13B2, the magnets may be arrayed in alternating polarities along rows that may be angled as desired relative to the X-direction. Other magnet arrangements may also be used.
Referring now to FIG. 13D1, there is shown a schematic view of a winding arrangement in accordance with another exemplary embodiment. In the exemplary embodiment shown in FIG. 13D1, two winding segments 1365A′, 1365B′ are illustrated, for example purposes, such as may be used for winding sets 1310, 1320, 1315, 1325 in
FIG. 13D2 shows another exemplary arrangement of individual winding for use with the disclosed embodiments. In FIG. 13D2 individual windings 1380 and 1385 may be oriented 90 degrees from each other and are positioned in an overlapping arrangement. Other suitable arrangements of windings are also contemplated.
Referring again to
where:
FAyj=KAM(y)iAj2−KAL(y)iAj cos [θA(x,z)+(2π/3)j], j=0,1,2 (4.4)
FByj=KBM(y)iBj2−KBL(y)iBj cos [θB(x,z)+(2π/3)j], j=0,1,2 (4.5)
utilizing the following nomenclature:
Fa=Total force produced in a-direction (N)
Fb=Total force produced in b-direction (N)
Fx=Total force produced in x-direction (N)
Fy=Total force produced in y-direction (N)
Fz=Total force produced in z-direction (N)
FAaj=Force produced by phase j of winding set A in a-direction, j=0, 1, 2 (N)
FAy=Total force produced by winding set A in y-direction (N)
FAyj=Force produced by phase j of winding set A in y-direction, j=0, 1, 2 (N)
FBbj=Force produced by phase j of winding set B in b-direction, j=0, 1, 2 (N)
FBy=Total force produced by winding set B in y-direction (N)
FByj=Force produced by phase j of winding set B in y-direction, j=0, 1, 2 (N)
IA=Amplitude of phase current for winding A (A)
IB=Amplitude of phase current for winding B (A)
iAj=Current through phase j of winding set A, j=0, 1, 2 (N)
iBj=Current through phase j of winding set B, j=0, 1, 2 (N)
KAa=Phase force constant of winding set A in a-direction (N/A)
KBb=Phase force constant of winding set B in b-direction (N/A)
KAL=Lorentz phase force constant of winding set A in y-direction (N/A)
KAM=Maxwell phase force constant of winding set A in y-direction (N/A2)
KBL=Lorentz phase force constant of winding set B in y-direction (N/A)
KBM=Maxwell phase force constant of winding set B in y-direction (N/A2)
x=Position in x-direction (m)
y=Position in y-direction (m)
z=Position in z-direction (m)
α=Angular orientation of winding set A (rad)
γ=Angular orientation of winding set B (rad)
ΔA=Electrical angle offset for winding set A (rad)
ΔB=Electrical angle offset for winding set B (rad)
θA=Electrical angle for winding set A (rad)
θB=Electrical angle for winding set B (rad)
RpA=Phase resistance of winding set A (Ohms)
RpB=Phase resistance of winding set B (Ohms)
β=Y-direction force balance factor between winding sets A and B (no units)
The following motor commutation equations for example may be utilized:
iAj=IA sin [θA(x,z)−ΔA+(2π/3)j], j=0,1,2 (4.6)
iBj=IB sin [θB(x,z)−ΔB+(2π/3)j], j=0,1,2 (4.7)
where IA, ΔA, IB, ΔB control magnitudes and orientations of force vectors produced by winding sets A and B.
It should be noted that equations (4.6) and (4.7) are similar to (3.3), (2.3), and (1.3) above. Thus, by adjusting the electrical angle θA, θB with the electrical angle offset ΔA, ΔB, the same motor commutation equations may be used for producing a one dimensional propulsion force in the x-direction, two dimensional forces including a propulsion force in the x-direction and a guidance force in the y-direction that may be substantially decoupled, and in this embodiment, three dimensional forces including propulsion forces in both the x-direction and a z-direction and a guidance force in the y-direction that may be substantially decoupled from each other.
In other words, by adjusting the electrical angle with the electrical angle offset, at least one, two, and three dimensional substantially independently controllable forces may be produced in the motor using a common set of commutation equations.
Sinusoidal phase currents in accordance with equations (4.4) and (4.5) can be generated, for example, for wye winding configurations using space vector modulation. The resulting motor forces may be expressed for example as:
Fa=1.5IAKAa(y)cos(ΔA) (4.8)
Fb=1.5IBKBb(y)cos(ΔB) (4.9)
Fx=Fa cos(α)+Fb cos(γ) (4.10)
Fz=Fa sin(α)+Fb sin(γ) (4.11)
Fy=1.5[IAKAL(y)sin(ΔA)+IA2KAM(y)+IBKBL(y)sin(ΔB)+IB2KBM(y)] (4.12)
In embodiments using displaced trapezoidal windings (see FIG. 13D1):
KAa(y)=KBb(y),KAL(y)=KBL(y),KAM(y)=KBM(y) (4.13)
γ=π−αFx=(Fa−Fb)cos(α),Fz=(Fa+Fb)sin(α) (4.14)
while in embodiments using orthogonal linear windings (see FIG. 13D2):
α=0,γ=π/2Fx=Fa,Fz=Fb (4.15)
The independent control parameters IA, IB and ΔA, ΔB for the winding sets may be for example:
IA=IA(Fa,FAy) (4.16)
ΔA=ΔA(Fa,FAy) (4.17)
IB=IB(Fb,FBy) (4.18)
ΔB=ΔB(Fb,FBy) (4.19)
where
Fa=(Fx sin γ−Fz cos γ)/(cos α sin γ−sin α cos γ) (4.20)
Fb=(Fx sin α−Fz cos α)/(sin α cos γ−cos α sin γ) (4.21)
The solution for (4.16) to (4.19) includes finding IA, ΔA, IB, and ΔB, given the desired forces Fx, Fz and Fy. This can be achieved for example by imposing the following “force balancing condition:”
are the y-direction force contributions of winding sets A and B, respectively. The parameter β represents the relative force contribution between the two winding sets along the y-direction. If for example β=1, then both winding sets have equal contributions for the y-force component. It is assumed that β is known at any point in time and it does not have to be constant.
In the exemplary embodiment, the motor control parameters may thus be expressed for example as:
The motor force coupling of the propulsion and guidance forces are represented as:
Referring still to
Electrical angle determination circuitry 1515 factors the a and b positions by 2π and the pitch of the windings to determine electrical angles θa and θb. A measured y position coordinate 1520 may be retrieved from sensors (similar to sensors 1390 1395
The embodiment of
As noted before, the following motor force equations may be defined for example as:
where
KAy=Phase force constant of winding set A in y-direction (N/A2)
KBy=Phase force constant of winding set B in y-direction (N/A2)
Also, the following motor commutation equations may be used:
iAj=IA sin [θA(x,z)+ΔA+(2π/3)j], j=0,1,2 (5.4)
iBj=IB sin [θB(x,z)+ΔB+(2π/3)j], j=0,1,2 (5.5)
As noted above, (5.4) and (5.5) are the same as (4.6) and (4.7), respectively, and are similar to (3.3), (2.3), and (1.3).) By adjusting the electrical angle(s) θA, θB of the winding sets with the electrical angle offset(s) ΔA, ΔB, the same motor commutation equations may be used for producing at least one, two, and three dimensional forces that are substantially decoupled from each other. As with other embodiments described herein, sinusoidal phase currents in accordance with Equations (5.4) and (5.5) may be generated using space vector modulation for example for wye winding configuration the winding sets.
The motor forces for example may be as follows:
Fa=1.5IAKAa(y)cos(ΔA) (5.6)
Fb=1.5IBKBb(y)cos(ΔB) (5.7)
Fx=Fa cos(α)+Fb cos(γ) (5.8)
(5.9)Fz=Fa sin(α)+Fb sin(γ) (5.9)
Fy=1.5[IA2KAy(y)+IB2KBy(y)] (5.10)
The motor force coupling of the propulsion and guidance forces are represented as:
For embodiments utilizing displaced trapezoidal windings:
KAa(y)=KBb(y),KAy(y)=KBy(y) (5.13)
γ=π−αFx=(Fa−Fb)cos(α),Fz=(Fz+Fb)sin(α) (5.14)
while for embodiments using orthogonal linear windings:
α=0,γ=π/2Fx=Fa,Fz=Fb (5.15)
The independent control parameters IA, IB and ΔA, IB for the winding sets A and B may be derived as:
IA=√{square root over (FAy/[1.5KAy(y)])} (5.16)
IB=√{square root over (FBy/[1.5KBy(y)])} (5.17)
ΔA=a cos {Fa/[1.5IAKAa(y)]} (5.18)
ΔB=a cos {Fb/[1.5IBKBb(y)]} (5.19)
where
Fa=(Fx sin γ−Fz cos γ)/(cos α sin γ−sin α cos γ) (5.20)
Fb=(Fx sin α−Fz cos α)/(sin α cos γ−cos α sin γ) (5.21)
Electrical angle determination circuitry 1615 factors the a and b positions by 2π and the pitch of the windings to determine electrical angles θa and θb. A measured y position coordinate 1620 may be retrieved from sensors (similar to sensor 1390, 1395
The embodiment of
In this case the motor force equations may before example expressed as:
The motor commutation equations may be for example as follows:
iAj=IA sin [θA(x,z)−ΔA+(2π/3)j] (6.5)
iBj=IB sin [θB(x,z)−ΔB+(2π/3)j] (6.6)
where again j=0, 1 and 2 represent phases 0, 1 and 2, respectively, and IA, ΔA, IB, ΔB are independent parameters to control magnitudes and orientations of force vectors produced by winding sets A and B.
As with the other embodiments, (6.5) and (6.6) are the same as (5.4) and (5.5), and (4.6) and (4.7), respectively, and are similar to (3.3), (2.3), and (1.3). By adjusting the electrical angle(s) θA, θB with the electrical angle offset(S) ΔA, ΔB, the same motor commutation equations may be used for producing at least one, two, and three dimensional forces decoupled from each other.
Sinusoidal phase currents in accordance with Equations (6.6) and (6.7) can be generated using space vector modulation for example for wye winding configuration.
The following motor force equations result:
Fa=1.5IAKAa(y)cos(ΔA) (6.7)
Fx=Fa cos(α)+Fb cos(γ) (6.8)
Fz=Fa sin(α)+Fb sin(γ) (6.9)
FAy=1.5IAKAy(y)sin(ΔA) (6.10)
FBy=1.5IBKBy(y)sin(ΔB) (6.11)
Fy=1.5[IAKAy(y)sin(ΔA)+IBKBy(y)sin(ΔB)] (6.12)
In an exemplary embodiment using displaced trapezoidal windings (see FIG. 13D1:
KAa(y)=KBb(y),KAy(y)=KBy(y) (6.13)
γ=π−αFx=(Fa−Fb)cos(α),Fz=(Fa+Fb)sin(α) (6.14)
while in an exemplary embodiment using orthogonal linear windings (see FIG. 13D2):
α=0,γ=π/2Fx=Fa,Fz=Fb (6.13)
To solve IA, ΔA, IB and ΔB in terms of Fx, Fy and Fz the force balance condition may be employed for example:
FAy=βFBy (6.14)
The parameter β may be known using certain criteria, for example as described below. The control parameters may thus be defined for example as:
Where for example:
Fa=(Fx sin γ−Fz cos γ)/(cos α sin γ−sin α cos γ) (6.19)
Fb=(Fx sin α−Fz cos α)/(sin α cos γ−cos α sin γ) (6.20)
The selection of the parameter β described in the embodiments above may be obtained by different optimization criteria. Depending on the types of forces involved, different criteria can be used. For example if only Lorentz forces are present, the force ratio criterion may be more appropriate. If the effect of back-electromotive forces (BEMF) is relevant, then the force ratio can be modified to account for that. If Maxwell forces are relevant as well, then the selection of β can be based on the ratio of phase amplitude currents. Additional criterion can be based on the powers consumed by the windings. The various criteria are explained below.
Assuming that only Lorentz forces are present, for example as in the embodiments described above, one possible criterion is to select β such that the contributions of winding sets A and B are chosen taking into account their maximum rated current and consequently their maximum rated forces along y-direction. This criterion may be expressed for example as:
Using the (6.16) condition,
A generalization of the criterion (7.1) may be obtained by taking into account the effect of BEMF, which limits the maximum possible phase current amplitudes to account for the bus or supply voltage (Vbus) being finite.
The maximum phase current amplitudes for winding sets A and B may be expressed for example in terms of the bus voltage, phase resistance, BEMF and motor speed as:
IAMax=Maximum rated amplitude of phase current for winding A (A)
IBMax=Maximum rated amplitude of phase current for winding B (A)
ωA=Mechanical angular speed for winding set A (rad/sec)
ωB=Mechanical angular speed for winding set B (rad/sec)
ρ=0.5 for a wye-wound winding set and
for a delta-wound winding set.
Using (7.5) and (7.6) in (7.2) and (7.3), β may be computed as:
which provides a criterion for a speed dependent β.
In the embodiments where Maxwell and Lorentz forces are present the relations between forces and currents are non-linear. In this situation it may be desired to establish a criterion based on the phase current amplitude ratios (rather than force ratios, see (7.1)) as described below.
The effect of BEMF can be included in the calculation of IAMax and IBMax as described above. The currents IA and IB are the solutions (6.18) and (6.20) or (4.57) and (4.59). The term β can be obtained from (7.8) after substitution of the appropriate solution.
In alternate embodiments, the phase current amplitude ratio may be convenient when the current-force relationship is linear, (e.g., when Lorentz forces are dominant) because it distributes the gap control force to the winding that is currently less utilized to provide propulsion. By way of example, considering that winding A provides force in the x-direction and winding B in the z-direction, when the system does not move in the x-direction and accelerates in the z-direction, winding A would provide larger portion of y-direction force. Conversely, if the system accelerates in the x-direction and does not apply much force in the z-direction, winding B would be providing larger portion of the y-direction force.
By way of example, an additional criterion that may be used:
where, Pd is the total power at the winding set d (d=A or B) and PdMax is the maximum rated power for winding set d (d=A or B).
Referring now also to
Fz=Total force in z-direction (N)
FzL=Force in z-direction produced by left motor (N)
FzR=Force in z-direction produced by right motor (N)
I=Amplitude of phase current (A)
ij=Current through phase j, j=0, 1, 2 (A)
K=Force constant (N/A)
Mx=Moment about x-axis (Nm)
p=Motor pitch (corresponding to electrical angle change of 2π) (m)
Rx=Rotation about x-axis (rad)
Δ=Electrical angle offset used for control purposes (rad)
θ=Electrical angle used for commutation purposes (rad)
The motor force equations may be expressed for example as:
and the motor commutation equation may for example be
ij=I sin [θ(z)+Δ+(2π/3)j−π/2], j=0,1,2 (8.3)
where I is a constant and Δ is a control parameter.
The resulting motor forces may for example be:
FzL=1.5IK sin(Δ) (8.4)
FzR=1.5IK sin(Δ) (8.5)
Fz=FzL+FzR=3IK sin(Δ) (8.6)
and hence the control parameter Δ may be established as
Δ=a sin [Fz/(3KI)] (8.7)
Referring to
where
θL=Electrical angle for left motor (rad)
θR=Electrical angle for right motor (rad)
ΔL=Electrical angle offset corresponding to displacement due to roll for left motor (rad)
ΔR=Electrical angle offset corresponding to displacement due to roll for right motor (rad)
and the following motor commutation equation may be used:
ij=I sin [θ(z)+Δ+(2π/3)j−π/2], j=0,1,2 (8.10)
where I is a constant and Δ is a control parameter.
The resulting motor forces and moment may for example be:
FzL=1.5IK sin(Δ−ΔL) (8.11)
FzR=1.5IK sin(Δ−ΔR) (8.12)
Fz=FzL+FzR=1.5IK[sin(Δ−ΔL)+sin(Δ−ΔR)] (8.13a)
Fz=1.5IK[sin Δ(cos ΔL+cos ΔR)−cos Δ(sin ΔL+sin ΔR)] (8.13b)
Mx=FzLdy/2+FzRdy/2=1.5IKdy/2[sin(Δ−ΔL)−sin(Δ−ΔR)] (8.14a)
Mx=1.5IKdy/2[sin Δ(cos ΔL−cos ΔR)−cos Δ(sin ΔL−sin ΔR)] (8.14b)
Considering in the example shown pure roll of the platform, i.e., rotation with respect to the x-axis, ΔL=−ΔR=ΔLR and:
Fz=3IK sin(Δ)cos(ΔLR) (8.15)
Mx=−1.5IKdy cos(Δ)sin(ΔLR) (8.16)
As may be realized, in the exemplary embodiment (e.g. of open-loop stabilization) the roll is expected to be small. Hence, for example |ΔLR| small the equation may be expressed as:
Fz=3IK sin(Δ) (8.17)
Mx=−1.5IKdy cos(Δ)ΔLR=−[1.5πIKdy2 cos(Δ)/p]Rx (8.18)
where Mx is a stabilization moment providing roll stiffness that depends on K, dy, p, I and Δ. (It should be noted that, in the exemplary embodiment, amplitude commutation may not provide a stabilization moment (Δ=π/2Mx=0).)
Hence, the control parameter Δ may be established as:
Δ=a sin [Fz/(3KI)] (8.19)
Similar as in Equation (8.7). Alternatively, amplitude I and phase Δ may be calculated together, in the exemplary embodiment, to keep roll stiffness constant. As another alternative, amplitude I may be used to produce Maxwell forces for guidance control in the y-direction.
Referring now to
where
FzF=Force in z-direction produced by front motor (N)
FzR=Force in z-direction produced by rear motor (N)
θF=Electrical angle for front motor (rad)
θR=Electrical angle for rear motor (rad)
ΔF=Electrical angle offset corresponding to displacement due to pitch for front motor (rad)
ΔR=Electrical angle offset corresponding to displacement due to pitch for rear motor (rad)
The following exemplary motor commutation equation may be used:
ij=I sin [θ(z)+Δ+(2π/3)j−π/2], j=0,1,2 (8.22)
where I is a constant and Δ is a control parameter
Accordingly, he resulting motor forces and moment may be expressed for example as:
FzF=1.5IK sin(Δ−ΔF) (8.23)
FzR=1.5IK sin(Δ−ΔR) (8.24)
Fz=FzF+FzR=1.5IK[sin(Δ−ΔF)+sin(Δ−ΔR)] (8.25a)
Fz=1.5IK[sin Δ(cos ΔF+cos ΔR)−cos Δ(sin ΔF+sin ΔR)] (8.25b)
My=FzFdx/2+FzRdx/2=1.5IKdx/2[sin(Δ−ΔF)−sin(Δ−ΔR)] (8.26a)
My=1.5IKdx/2[sin Δ(cos ΔF−cos ΔR)−cos Δ(sin ΔF−sin ΔR)] (8.26b)
where
My=Moment about y-axis (Nm)
Considering in the example shown pure pitch of the platform, e.g., rotation with respect to the y-axis only, as illustrated in
Fz=3IK sin(Δ)cos(ΔFR) (8.27)
My=−1.5IKdx cos(Δ)sin(ΔFR) (8.28)
Similar to the approach of open loop roll stabilization discussed before, in the exemplary embodiment illustrated of open loop pitch stabilization, the pitch of the platform is expected to be small.
Thus, |ΔFR|=small
and accordingly
Fz=3IK sin(Δ) (8.29)
My=−1.5IKdx cos(Δ)ΔFR=−[1.5πIKdx2 cos(Δ)/p]Ry (8.30)
where
Ry=Rotation about y-axis (rad)
and My is a stabilization moment providing pitch stiffness that depends on K, dx, p, I and Δ. (As mentioned above, it should be noted that in the exemplary embodiment amplitude commutation may not provide stabilization moment (Δ=π/2My=0).)
The control parameter Δ may thus be established as:
Δ=a sin [Fz/(3KI)] (8.31)
Similar as in Equation (8.7). Similar to what was previously described, in the alternative, amplitude I and phase Δ may be calculated together in the exemplary embodiment to keep pitch stiffness constant. As another alternative, amplitude I can be used to produce Maxwell forces for guidance control in y-direction.
In the exemplary embodiment the force distribution may be expressed for example as:
fz(x)=1.5KI sin [Δ−ΔP(x)]=1.5KI[sin Δ cos ΔP(x)−cos Δ sin ΔP(x)] (8.32)
where
fz=Distribution of z-force (N/m)
ΔP=Electrical angle offset corresponding to displacement due to pitch (rad)
Considering small pitch angle and, therefore, |ΔP|=small:
fz(x)≈1.5KI[sin(Δ)−cos(Δ)ΔP(x)]=1.5KI{sin(Δ)−[2πRy cos(Δ)/p]x} (8.33)
The total force and moment may be expressed for example as:
where My is a stabilization moment providing pitch stiffness that depends on K, dx, p, I and Δ. (As described before, the amplitude commutation may not provide stabilization moment (Δ=π/2My=0).)
The control parameter may be established as:
Δ=a sin [Fz/(1.5KIdx)] (8.36)
Similar to embodiments above, in the alternative, amplitude I and phase Δ may be calculated together in the exemplary embodiment to keep pitch stiffness constant. As another alternative, amplitude I can be used to produce Maxwell forces for guidance control in the y-direction. In alternate embodiments, applicable equally to all of the roll and pitch stabilization cases similar to those previously described, this mechanism can be used to control stiffness in a closed loop manner, provided that roll or pitch measurements are available for feedback use. This nonetheless would keep the controls hardware simple on the motor amplifier side.
In the exemplary embodiment illustrated, the control system 1900 may perform commutation of the windings of forcer 2115 to effect control of the platen or transport apparatus 2135 (similar to apparatus 1305 in
The embodiments disclosed above provide sets of motor force equations, motor commutation equations, and expressions for calculation of motor control parameters based on specified propulsion and guidance forces, for both two dimensional and three dimensional motor configurations. The disclosed embodiments include adjusting an electrical angle used to drive a common set of commutation functions with an electrical angle offset so that the same motor commutation functions may be used for producing at least a one dimensional propulsion force in the x-direction, two dimensional forces including a propulsion force in the x-direction and a guidance force in the y-direction, and three dimensional forces including propulsion forces in both the x-direction and a z-direction and a guidance force in the y-direction. In addition, motor force equations, motor commutation equations, and motor control parameter calculations are provided for phase commutation with open loop stabilization, including open loop roll stabilization, open loop pitch stabilization with discrete forces, and open loop pitch stabilization with distributed forces.
It should be understood that the foregoing description is only illustrative of the invention. Various alternatives and modifications can be devised by those skilled in the art without departing from the invention. Accordingly, the present invention is intended to embrace all such alternatives, modifications and variances which fall within the scope of the appended claims.
Hofmeister, Christopher, Hosek, Martin, Moura, Jairo Terra
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